If you want to do the official body pump workout it is unlikely that you'll find it in a cheaper gym. The gym has to pay for the license to teach these branded workouts.

Check out the public Centres Sportifs as they may have a very similar, but unbranded workout. 

You could also look at the gym City Green, just over the French border towards Hermance. They have all the Les Mills workouts, it's supposed to be a great gym and might be a bit cheaper, as it's in France

Check this one at American Fitness in Acacias/Geneva . It is linked to a Groupon offer

http://www.groupon.ch/deals/geneva_en/american-fitnessEN/800189

You may also ask for a week trial at a reduced rate just to be sure.

Hi Alfi. That's a great deal, I checked it out as I wouldn't mind a gym membership myself. The small print says 'voucher must be redeemed between September and December'. Be careful with Groupon!

@Amy:   Who knows? Contacting American Fitness yourself now you could end up with an introductory offer at a discount especially if you both with Daphne could sign up...Thought wise people say "You never loose by trying"  ;)